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Abstract— In this paper optimization of routing in ad-hocnetworks is surveyed and a new method for reducing the complexityof routing algorithms is suggested. Using binary matrices for eachnode in the network and updating it once the routing is done, helpsnodes to stop repeating the routing protocols in each data transfer.The algorithm suggested can reduce the complexity of routing to theleast amount possible.Keywords— Ad-hoc Networks, Algorithm, Protocol, RoutingTrain.I.INTRODUCTIOND-HOC networks are getting popular for their ease andspeed in deployment, decreased dependence oninfrastructure, being the only possible solution to interconnecta group of nodes and many commercial products availabletoday.A.TerminologyAd hoc network is a collection of wireless nodes that candynamically be set up anywhere and anytime without usingany pre-existing network infrastructure [1, 2, 3, 4, 5]. Themajor characteristics of ad hoc networks are dynamictopologies, being bandwidth-constraint, energy-constrainedoperation, and limited physical security [6, 7].B.Prevalent ProtocolsSome of the most common routing protocols are named andaddressed bellow:Destination Sequenced Distance Vector (DSDV) is a table-driven/ proactive protocol in which routing is done by usingthe Bellman-Ford Algorithm [10] for each node by theinformation which exists at their tables [1].Clusterhead-Gateway Switch Routing (CGSR) is a table-driven/proactive protocol in which cluster-heads are selectedMas'ood Kargar is with the Department of Computer Engineering, IslamicAzad University of Tabriz Branch, Tabriz, Iran. He is also collaborating inIslamic Azad University of Tabriz Branch Computer Research Laboratories.IAUT-CRL (phone: +98-9141035597; email: kargar@iaut.ac.ir).Farzaneh Fartash is with the Department of Information TechnologyEngineering, International University of Chabahar (phone: +98-9141002139;e-mail: fartash@iuc.ac.ir).Taha Saderi is with the Department of Computer Engineering, IslamicAzad University of Tabriz Branch (phone: +98-9143165992; e-mail:saderi@iaut.ac.ir).Mohammad Ebrahimi Dishabi is with the Department of ComputerEngineering, Islamic Azad University of Miyaneh Branch, Miyaneh, Iran.(email: mrebrahimy@m-iut.ac.ir).using an election. The route is found through cluster-headswhich is usually done by DSDV Protocol [1].Optimized Link State Routing (OLSR) is a table-driven/proactive protocol in which routing is done by usingthe Dijkstra Algorithm [10] for each node by the informationwhich exists at their tables [11, 12].Wireless Routing Protocol (WRP) is a table-driven/proactive protocol in which each node sends a hellomessage to its neighbors and considers them as its successorsand does this job till reaches the destination [13].Zone Routing Protocol (ZRP) is a hybrid protocol in whicheach node denotes route request from the nodes in its zone.The node which has the destination node in its zone denotesroute reply [8].Dynamic Source Routing Protocol (DSR) is an on-demand-driven/reactive protocol in which routing is done by thepacket propagation through the network [1, 2, 4, 12, 14, 15,16, 17]. For further information about packet broadcastingrefer to [18].Ad-hoc On-demand Distance Vector Routing (AODV) is anon-demand-driven/reactive protocol. It is just like DSR. Thedifference between this protocol and DSR is in hello messageswhich make AODV reply faster when there is no route to thedestination [4, 12, 14, 16, 17, 18].Temporally-Ordered Routing Algorithm (TORA) is an on-demand-driven/reactive protocol. It uses three packets: query,update and clear [14, 16]. So the whole graph is updated foreach node after the questioning has finished.Landmark Routing (LANMAR) is a cluster-based/hierarchical protocol. It uses some nodes as land-marksand finds the destination by their guidance [20].Core-Extraction Distributed Ad-hoc Routing (CEDAR) is acluster-based / hierarchical protocol. It sets a dominator foreach cluster and the nodes do questioning from thedominators. After finding the routes they give the nodes theroutes they should pass [21].C.The ProblemRouting protocols in ad hoc networks are divided into fourmain groups: 1-Table-Driven / Proactive, 2-Hybrid, 3-On-Demand-driven /Reactive, 4-Clusterbased / Hierarchical [8].Each group contains so many routing algorithms with specialadvantages and disadvantages in comparison with others.Some of the mostly used ones have been studied andoptimized, resulting in certain methods, theories, andalgorithms. The problem with most of these optimizingA Theory in Optimization of Ad-hoc RoutingAlgorithmsM. Kargar, F.Fartash, T. Saderi, M. Ebrahimi DishabiAWorld Academy of Science, Engineering and Technology 48 2008260algorithms, however, is that they have been produced forspecial protocol and can not be used on the others.D.SolutionHere we suggest a new way for optimizing routingprotocols by training the network. In this method, after aperiod of time, the complexity of routing protocol reduces tothe most optimized range. Obviously running the routingprotocols for n-times is not a good idea. In all protocols wealways want to find the optimized way to reduce the timespent. Therefore if we repeat optimizing for n-times then it isan overhead itself. As a solution a new method for reducingthe times that the routing protocols are repeated, is suggested.Although the presented algorithm is no more than a theory andhasn't been practiced, but we think it will help a lot if itbecomes accepted, simulated and finally examined.E.The ClaimWe claim that such a solution does exist. By using binarymatrices for each node in the network and finding a routethrough running a routing protocol and at last updating thematrices considering the route given, fulfils the need forrepeating the routing protocols in each data transfer. Forfurther information about rerouting in the protocols refer to[9].F.ObjectiveThe objectives we want to achieve by suggesting a newmethod is complexity reduction in routing algorithms. By thistheory, we reach to a point that the nodes do not need to askfor the route and they learn the way that they should send theirdata. So only the nodes on the route are visited and the data ispassed through them.G.Paper outlineThis paper is organized in four sections. In Section 1 westarted the problem, an idea solution to the problem and ourclaim regarding the solution. In Section 2 we speak about theworks done for routing optimization and address some ofthem. In section 3 the Training Algorithm is given and itsbenefits are described. In section 4 the reason of suggestingnew method in the ad hoc networks is concluded.II.PREVIOUS WORKAlthough there are some works and surveys done for theoptimization of routing or increase in security of ad-hocnetworks but still there are shortages to be fulfilled. Some ofthe papers describing the jobs done for routing optimizationare mentioned and introduced below as the previous work forour suggestion in this paper.In [22] a model of life time route optimization in wirelessad-hoc networks has been surveyed. The route lifetime valueis one of the most important parameters for the design of anon-demand ad-hoc routing protocol. This parameterdetermines the duration of an active path/route in the routingtable to transmit the packets reliably. This is to ensure that therouting table does not attempt to discover a new route and/ordelete an existing active route within its lifetime. So, too longroute lifetime may lead to retardation in updating the routingtable even though some paths are broken [22].In the referred paper, adaptive route lifetime determinationthrough a fuzzy logic system is proposed. Fuzzy logic ischosen due to the uncertainty associated with node mobilityestimation and drawbacks of mathematical models. Definitionof fuzzy sets (membership functions) and a set of rules (rule-base) have been proposed to design the new method, calledfuzzy ART. This new method is evaluated with the AODVrouting protocol, we believe it can be generalized for other ad-hoc routing protocols, as well [22].In [23] a Dynamic Source Routing Protocol using SelfHealing and Optimizing Routing Technique based on fuzzylogic concepts is presented. The paths generated byconventional dynamical source routing protocol deviate farfrom the optimal paths because of the lack of knowledgeabout the global topology and the mobility of nodes. Routingoptimality affects the network performance, especially whenthe load is high. Longer route consumes more bandwidth,power and is more prone to disconnections. Self Healing andOptimizing Routing Technique (SHORT) is a technique thatmonitors the route and tries to shorten it, if a short-cut isavailable. The proposed fuzzy logic method is evaluated andcompared with conventional method using GloMoSim [23].In [24] the work concentrates particularly on securingrouting protocols, which are still immature and under rapiddevelopment. Because of high dynamics and other limitsshown before, the design of ad-hoc routing protocols is morecomplicated and usually a nice piece of trade-off amongmultiple factors, which include improving routing optimum,minimizing traffic volume and restricting power use. Thougha lot of new protocols have been proposed and implemented,we understand that security issues are rarely concerned oreven so, hardly practical [24].In [25] time-slots are assigned for each node in the networkto access the control channels so that it is guaranteed that eachnode can broadcast the control packet to any one-hopneighbor in one scheduling cycle. The objective is tominimize the total number of different time-slots in thescheduling cycle. It leads to a determined access schedulingon the control channels. Each node is assigned with one /several chance(s) (time-slot in a TDMA system) to access thecontrol channel, and the broadcasting on the assigned time-slots is guaranteed to be received correctly by its neighbor(s).The access delay on the control channels is upper-bounded bythe length of the scheduling cycle. Note that a single time-slotcan be reused by two nodes if they do not interfere with eachother. The objective of the access scheduling problem is tominimize the length of the scheduling cycle [25].In [26] three major optimization schemes for the well-known AODV routing protocol are described in order to getsome of the proactive protocols features in it. The describedschemes are: Reverse path setup, Forward path setup andRoute Scattering. The targeted characteristics are: trafficindependent control and shortest path routes.World Academy of Science, Engineering and Technology 48 2008261In [27] routing optimality using different metrics such aspath length, energy consumption along the path, and energyaware load balancing among the nodes are defined and aframework of Self-Healing and Optimizing RoutingTechniques (SHORT) for mobile ad hoc networks isproposed. While using SHORT, all the neighboring nodesmonitor the route and try to optimize it if and when a betterlocal sub-path is available. Thus SHORT enhancesperformance in terms of bandwidth and latency withoutincurring any significant additional cost. In addition, SHORTcan be also used to determine paths that result in low energyconsumption or optimize the residual battery power.III.TRAINING ALGORITHMA.Algorithm RepresentationAs described above, all routing algorithms mostly optimizethe route found and pay less attention to the reduction ofcomplexity in routing. The protocol used should repeat therouting every time that data transfer is required. Of coursesome optimizations are done such in DSR [28] but the mainproblem of these optimization methods is that they are justspecific for the protocol given. In the method used foroptimizing the DSR protocol, a cache is used for saving thepassed route and routing may be repeated for some times.The algorithm that we suggest here is protocol-free. It canbe adjusted in all routing protocols and we can say it is highlevel. It can also use different routing protocols in onenetwork. In fact we are training the network to learn fromrouting and after doing the routing protocol for a few timesthe nodes themselves know that from which route they shouldtransfer data. This is the time when the complexity of routingfor transferring data, reduces to "L" which is the exact routedistance from source to destination. In other words instead ofrunning O(V*E) times we run O(L) times which equals withthe number of the edges that should be passed. This is themost optimized complexity a programmer or manufacturermay seek for.In addition, in this algorithm, not only we have thoughtabout the time cost, but also we have used a binary matrix intraining, that reduces the memory cost to minimum and helpsthe training period of time to be spent so fast.Before writing the algorithm, the suppositions at thenetwork are mentioned:1- The network is supposed to be a graph with nodes andedges.2- Nodes are represented by numbers.3- The edges from one node to its neighboring nodes arenumbered consequently. By giving a number for each node,the ordering of edges becomes easier. Of course the number ofnodes related to one node needn't be serial.4- Each node has an array for training and an array forcontrolling bandwidth and traffic. The bandwidth array is notused in training and it is just for controlling which increasesthe transferring quality. Using table for saving the informationby most of the protocols makes the algorithm easy to setup.5- There is one adjacent matrix for the whole graph.6- "G" is the graph, "w" is the weight, "s" is the source, "d"is the destination, "R" is the matrix for routing and "Ro" is theroute array.Here is the code of Training Algorithm:Training_Algorithm (G,w,s,d)If ! R[d]Ro = get_route_from_a_routing_algorithm(G,w,s,d)send_update(G,Ro,0,d)------------------------------------Send_data(data,s,d)Training_ Algorithm (G,w,s,d)Transfer_data(data,s,d)------------------------------------Transfer_data(data,s,d)If s <> dJ=index_vertex(s, lg R[d])Transfer(data,j,d)------------------------------------Send_update(G,Ro,start,d)If Ro[start] <> dK=index_Edge(Ro[start], Ro[start+1])R[d]=2^kSend_update(G,Ro,start+1,d)------------------------------------Index_Edge(i,j) As integerK=0Flag = falseWhile (flag)DoIf A[i][k]Counter=counter+1K=k+1If (counter=j)Flag=falseReturn counter------------------------------------Index_vertex(i,k) As integerK=0Flag = falseWhile (flag)DoIf A[i][k]Counter=counter+1L=L+1If (counter=k)Flag=falseReturn LAs it is shown, before data transfer, first the algorithmchecks that if the graph is trained or not. If it is trained, thendata is sent, else it gets route as an array from a routingprotocol. After this, it trains the nodes by sending updatethrough the route given. In fact updating does the job oftraining.World Academy of Science, Engineering and Technology 48 2008262Each node has a binary matrix with one dimension. Therows of that matrix or the indexes of the array show thenumeric label of each node. The bits given in rows show theedge that the node can send its data through it. By usinglogarithm and powering in the algorithm, the binary matrixcan be filled so easily. In addition, using the binary matrixtakes less memory cost and the access takes O(1) times andthis causes the training and routing operations run simply.Figure1 provides an example.1 2 3 4 50 2 1 2 411 2 3 4 50 0 1 1 121 2 3 4 50 1 0 1 131 2 3 4 50 1 1 0 241 2 3 4 50 1 1 1 05Fig.1 A sample for the matrices designed forthe arrays of the nodes in a graph G.While sending update, the matrix in each node on the routeis updated. For example if the route from 1 to 2 first passesfrom 4, and the edge from 1 to 4 is the second edge of 1, thenin the matrix at the fifth row the number [9]2(=[2]10) shouldbe written; which means from 1 to 2 we should pass thesecond edge.The function index_edge gets the two adjacent nodes andgives the number of edge between them which is ordered bythe number of the nodes. For instance in order to find out thatthe second edge of 1 is related to which node, we refer to theadjacent matrix.Figure2 provides the adjacent matrix for the graph above.00100100100100000100111005432154321Fig. 2 A sample for the adjacent matrix designed for the graph G.In the adjacent matrix the algorithm counts the number of1s and the number of the comparing operation repetition. Atthe matrix in the example when it reaches to the second 1, ithas done the comparing operation for 4 times. So it recognizesthat the second edge of node 1 is related to the node 4.Therefore in order to reach to the node 2, it should pass thenode 4.The function index_vertex gets the number of a node andan edge connected to it and gives the number of the adjacentnode related to that edge. To find the order of the edge, thisalgorithm uses logarithm in the basis of 2. In the exampleabove (log 100) equals with 3 which means to the mentionednode we should pass the third edge. By this method we avoidthe overload of clustering and the high complexity of for-loop.We have also an adjacent matrix for the whole graph whichits memory cost in a graph with so many nodes would beinconsiderable though its processing would be timeconsuming.While the data transferring is active and one of the nodesruns away from the network, the number of rows in trainingmatrix in which the route passes from that node (the numberof the edge related to that node is 1) sets to zero. So therouting and training algorithms for the related destinationsshould be repeated.2122134512132G010001000001000543210000000000000005432100100000000000054321000000000000000543210001000100000000054321World Academy of Science, Engineering and Technology 48 2008263B.Benefits of Using This MethodAs it is mentioned, this algorithm doesn’t optimize therouting protocol, but it guides and trains the network to learnthe protocol once and use the route given for thousands oftimes. In addition while sending update amongst the routefound, the nodes on the route are also updated. The importantpoint is that if the destination is far from the source and itpasses through the most of the nodes, then large amount ofnodes become updated and this causes less repetition ofrouting protocol.Being protocol-free, this method can be theoreticallyapplied in all kinds of mobile or wireless ad-hoc networks andthere would be no limitation in using this algorithm.Propagating packets or messages for requesting andreplying through the network causes the traffic to be heavier.But in our method after initial routing we never use suchpackets or messages.As it is said before, the time complexity reduces to "L" aftertraining, which means that the data has been transferredthrough the right path. Using the binary matrix for each node,the memory complexity for n nodes is n bytes. Less memoryoccupied and less time spent, makes this method a desirableway in data transfer on networks)IV.CONCLUSIONSRepeating the routing protocols for each node is a timeconsuming task. Currently applicable algorithms, in thisregard, suffer from a high complexity of time which isdiscussed in section 2. In section 3 we have introduced a newalgorithm, which by training the network reduces the numberof times that the routing protocols are being repeated. After afew repetition of routing the nodes themselves learn fromwhere they should send data.A.Future WorkThe method we presented in this paper sets the stage readyfor an interesting topic of research: Traffic Control on Ad-Hoc Networks. A New Approach:The algorithm introduced in this paper can set thebandwidth array, in addition to the training. The bandwidtharray is adjusted to control the traffic of the route. Whilesending data and routing to the destination the algorithmincrements a counter. This means that the path from the sourceto the destination has been used for the number of times thecounter shows. Now, if we notice that one path is used somany times and one less, we can maintain the bandwidth ofthe path. This is a good way to control the traffic on thenetwork. If the bandwidth has reached to the highest amount,new edges may be produced. It seems to be a good idea tomanage the traffic on the network.ACKNOWLEDGMENTWe would like to thank Dr. Ayaz Isazadeh, Dr. Mir KamalMirnia and Dr. Ahamad Habibizad Navin for his guidance andtrue helps in preparing the paper.REFERENCES[1] I. Stojmenovic, “Position-Based Routing in Ad Hoc Networks”, IEEECommunications Magazine, pp. 2-3, July 2002.[2] L. Barriere, P. Fraingniaud and L. Narayanan, “Robust Position-BasedRouting in Wireless Ad Hoc Networks with Unstable TransmissionRanges”, Rome, Italy 2001 ACM, p.19.[3] L. Zhou and Z. J. Haas, “Securing Ad Hoc Networks”, IEEE network,special issue on network security, p.1, November/December, 1999.[4] S. P. Kon and R. V. Boppana, “On Reducing Packet Latencies in AdHoc Networks”, The University of Texas at San Antonio, WCNC 2000.[5] Y. Hu, A. Perrig and D. B. 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